Question

I can't understand this question please help me to solve it​

Answer 1

Answer:

Step-by-step explanation:) Let G and H be the mid-points of side AB and AC respectively.

Line segment GH is joining the mid-points. Therefore, it will be parallel to third side BC and also its length will be half of the length of BC (mid-point theorem).

⊥ GH = 1/2 BC and GH || BD

⊥ GH = BD = DC and GH || BD (D is the mid-point of BC)

Consider quadrilateral GHDB.

GH ||BD and GH = BD

Two line segments joining two parallel line segments of equal length will also be equal and parallel to each other.

Therefore, BG = DH and BG || DH

Hence, quadrilateral GHDB is a parallelogram.

We know that in a parallelogram, the diagonal bisects it into two triangles of equal area.

Hence, Area (ΔBDG) = Area (ΔHGD)

Similarly, it can be proved that quadrilaterals DCHG, GDHA, and BEDG are parallelograms and their respective diagonals are dividing them into two triangles of equal area.

ar (ΔGDH) = ar (ΔCHD) (For parallelogram DCHG)

ar (ΔGDH) = ar (ΔHAG) (For parallelogram GDHA)

ar (ΔBDE) = ar (ΔDBG) (For parallelogram BEDG)

ar (ΔABC) = ar(ΔBDG) + ar(ΔGDH) + ar(ΔDCH) + ar(ΔAGH)

ar (ΔABC) = 4 × ar(ΔBDE)

Hence, ar (BDE) = 1/4 ar (ABC)

Let H be the height of vertex A, corresponding to the side BC in ΔABC.

Let h be the height of vertex E, corresponding to the side BD in ΔBDE.

it was shown that ar (BDE) = 1/4 ar (ABC)

therefore , 1/2 bd *h = 1/4 *1/2 bc*H

bd*h=1/4 *2bd *H

h=1/2 H

therefore ar(fed)=1/2 ar (afc)